1.1 Measurements of the Eye's Aberrations
There are several objective optical techniques that have been used to measure the wavefront aberrations of the eye. The aberroscope, which is disclosed by Walsh et al. in the Journal of the Optical Society of America A, Vol.1, pp. 987-992 (1984), projects a nearly collimated beam into the eye which is spatially modulated near the pupil by a regular grid pattern. This beam images onto the retina as a small bright disk which is modulated by the dark lines of the grid pattern. Since the eye's pupillary aberrations distort the retinal image of the grid pattern, measurements of the distortions on the retina reveal the pupillary aberrations.
The spatially resolved refractometer, which is disclosed by Webb et al. in Applied Optics, Vol. 31, pp. 3678-3686 (1992), projects a small diameter collimated beam through the eye's pupil. Instead of being spatially modulated by a physical grid as with the aberroscope, the spatially resolved refractometer's beam is raster-scanned across the entire pupil. A sequence of retinal images of the focused light is recorded with each image associated with a particular location at the pupil. A mapping of the relative locations of these retinal images reveals the aberrations across the pupil.
Analyzers of retinal point-spread functions have been disclosed by Artal et al. in the Journal of the Optical Society of America A, Vol. 5, pp. 1201-1206 (1988). Analyzers of retinal line-spread functions have been disclosed by Magnante et al. in Vision Science and Its Applications, Technical Digest Series (Optical Society of America, Washington, D.C.), pp. 76-79 (1997). When used to measure the wavefront aberrations of the eye, these spread function analyzers project a small diameter circular beam into the eye at the center of the pupil. This beam focuses onto the retina as a tiny source of light. The light from this tiny retinal source scatters back through the dilated pupil. A small circular aperture (approximately 1 mm diameter) in the imaging section of the analyzer is located conjugate to the pupil plane. This aperture may be translated up/down or side/side to sample specific regions in the pupil plane where wavefront aberration measurements are sought. An imaging lens focuses the light through the small aperture onto the imaging plane of a camera. Measurements of the relative locations of the focal spots for the various locations of the small aperture characterize the pupillary wavefront aberrations.
The Hartmann-Shack wavefront sensor for ordinary lens or mirror testing was disclosed originally by Shack et al. in the Journal of the Optical Society of America, Vol. 61, p. 656 (1971). This type of wavefront sensor was adapted to measure the wavefront aberrations of the eye by Liang et al., Journal of the Optical Society of America A, Vol. 11, pp. 1949-1957 (1994). The Hartmann-Shack wavefront sensor is similar to point-spread (or line-spread) function analyzers in that: 1) it projects a fine point of light onto the retina through a small diameter pupil of the eye, and 2) the light which is scattered back from the retina through the eye's pupil is imaged onto a camera with a lens that is conjugate to the eye's pupil. However, instead of using a single lens with a moveable small aperture to image the retinal image onto the camera, the Hartmann-Shack wavefront sensor utilizes a regular two-dimensional array of small lenses (commonly called a microlens array) which is optically conjugate to the eye's pupil to focus the back scattered light from the retinal image onto the camera. Typical diameters of individual microlenses range from 0.1 to 1.0 millimeter. With the Hartmann-Shack wavefront sensor, instead of having a single spot of light corresponding to a single aperture imaged by the camera, there is an array of focused spots imaged by the camera . . . one spot for each lens in the microlens array. Furthermore, each imaged spot of light corresponds to a specific location at the eye's pupil. Measurements of the locations of the array of imaged spots are used to quantify the pupillary aberrations.
Measurements of the wavefront aberrations of the eye to a high degree of precision using an improved Hartmann-Shack wavefront sensor are described in 1998 U.S. Pat. No. 5,777,719 to Williams and Liang. What is described in U.S. Pat. No. 5,777,719 improves upon what was described previously by Liang et al. in the Journal of the Optical Society of America A, Vol. 11, pp. 1949-1957 (1994). Device improvements described in the Williams and Liang 1998 Patent include: 1) a wavefront correcting deformable mirror, 2) a method to feedback signals to the deformable mirror to correct the wavefront aberrations, and 3) a polarizer used with a polarizing beamsplitter to reduce unwanted stray light from impinging on the recording camera.
Although the precision of the resulting wavefront aberration measurements cited by Williams and Liang is impressive, the implementation of a deformable mirror and a feedback loop is very costly and is not necessary for achieving the purposes of my invention.
Furthermore, the polarizer with polarizing beamsplitter cited in the Williams and Liang patent are not necessary for achieving the purposes of my invention, and those devices are replaced in my invention with a single device called an optical isolator (consisting of a polarizer fused to a quarter-wave plate). The optical isolator achieves the same purpose as the pair of polarizing devices described by Williams and Liang, namely reducing unwanted stray light.
Finally, a laser is cited as the preferred illumination source in the Williams and Liang patent. However, a conventional laser is improved upon in my invention through the use of a diode laser operated below threshold. Such a light source is not as coherent as a standard laser operating above threshold, Images formed with such a non-coherent source are less granular (having less "speckle") than those formed by coherent sources. This improvement results in less noisy granularity in the microlens images and, thereby, improves the accuracy of the image processing which depends on precisely locating the microlens images.
1.2 Analysis of Hartmann-Shack Wavefront Sensor Data to Characterize the Eye's Optical Aberrations
The essential data provided by a Hartmann-Shack wavefront sensor modified to measure the human eye are the directions of the optical rays emerging through the eye's pupil. The method of deriving a mathematical expression for the wavefront from this directional ray information is described by Liang et al. in the Journal of the Optical Society of America A, Vol. 11, pp. 1949-1957 (1994). It is also the method cited in 1998 U.S. Pat. No. 5,777,719 to Williams and Liang. First, the wavefront is expressed as a series of Zernike polynomials with each term weighted initially by an unknown coefficient. Zernike polynomials are described in Appendix 2 of "Optical Shop Testing" by D. Malacara (John Wiley and Sons, New York, 1978). Next, partial derivatives (in x & y) are then calculated from the Zernike series expansion. Then, these partial derivative expressions respectively are set equal to the measured wavefront slopes in the x and y directions obtained from the wavefront sensor measurements. Finally, the method of least-squares fitting of polynomial series to the experimental wavefront slope data is employed which results in a matrix expression which, when solved, yields the coefficients of the Zernike polynomials. Consequently, the wavefront, expressed by the Zernike polynomial series, is completely and numerically determined numerically at all points in the pupil plane. The least-squares fitting method is discussed in Chapter 9, Section 11 of "Mathematics of Physics and Modern Engineering" by Sokolnikoff and Redheffer (McGraw-Hill, New York, 1958).
Although the above described methods to calculate the aberrated wavefront of the eye are cited in the Williams and Liang patent, it is significant to note that there is not any description in their patent of how to design an aberration-correcting contact lens or corneal surface from the aberrated wavefront data. These details for designing an aberration-correcting contact lens or corneal surface are not obvious, and require a number of complex mathematical steps. These mathematical details for designing aberration correcting surfaces on contact lenses or on the cornea itself are described fully in my invention.
Furthermore, Williams and Liang demonstrate that the eye's aberrations can be corrected by properly modifying the surface of a reflecting mirror. However, they do not demonstrate or provide any description of how aberration-correcting surfaces can be designed on refractive surfaces such as those on contact lenses or on the cornea itself. My invention gives a detailed mathematical description of how to design such refracting optical surfaces that correct the eye's aberrations.
1.3 Fabrication of Conventional Contact Lenses
Conventional contact lenses with spherical or toroidal surface contours are made routinely using a method called single point diamond turning which utilizes very precise vibration-free lathes. The contact lens blank rotates on a spindle while a diamond point tool, moving along a precise path, cuts the desired surface contour. The end result is a surface which does not need additional polishing, and exhibits excellent optical qualities in both figure accuracy and surface finish. Figure accuracy over the lens surface is better than one wavelength of light. Surface finish, which is reported as rms surface roughness, is better than 1 microinch. Machines of this type and their use are described by Plummer et al. in the Proceedings of the 8.sup.th International Precision Engineering Seminar (American Society of Precision Engineering, pp. 24-29, 1995).
1.4 Corneal Tissue Ablation to Correct Vision
With the advent of the excimer laser, the means are available for refractive surgeons to flatten and reshape the surface of the cornea in order to improve vision. The excimer laser selectively removes microscopic layers of corneal tissue allowing light rays to focus more sharply on the retina. In the procedure known as photorefractive keratectomy (PRK), the laser ablates tissue on the surface of the cornea. In the procedure known as laser in-situ keratomileusis (LASIK), the surgeon first creates a flap on the cornea and then uses the laser to reshape tissue below the corneal surface. Layers of tissue as thin as 0.25 microns can be ablated.
With current laser procedures, it is possible only to correct relatively coarse or low order aberrations of the eye, namely high levels of nearsightedness, and moderate amounts of farsightedness and astigmatism. With the analytical methods of my invention, which take into account the corneal shape, and both the low order and higher order aberrations of the eye, a modified corneal shape is found which allows all rays from external point objects to focus sharply on the retina. By the means offered by my invention, refractive surgery procedures to improve vision will be improved greatly.